In a nutshell, when it comes to Roots and Negatives, if you're dealing with an even root, you cannot put a negative number under the radical. Full stop. For example...

$\sqrt{-5} =$ no good

$\sqrt[4]{-11} =$ no bueno

$\sqrt[100!]{-36} =$ अच्छा नहीं

However, if you're dealing with an odd root, you can put a negative (or positive) number under the radical. For example...

$\sqrt[3]{-5} =$ no problem

$\sqrt[5]{-11} =$ no problema

$\sqrt[3^{100}]{-36} =$ कोई बात नहीं

An Important Exception

If there is an even exponent under the radical, you can do whatever you want. You can put a positive number, a negative number, zero, whatever. This is because you do the exponent operation before the root operation, and the even exponent causes the negative number to become positive. This is why the square root of $x^2$ equals $|x|$. If you don't know what those two lines mean, check out the quant mountain entry on Absolute Value.

$$\sqrt{x^2} = |x|$$

$\sqrt[6]{(-5)^4}=$ no problem